Cost-Based Droop Scheme with Lower Generation Costs for Microgrids

Inam Ullah Nutkani1,2, Poh Chiang Loh2,3 and Frede Blaabjerg3

iExperimental Power Grid Centre, Agency for Science, Technology and Research, Singapore 2School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore

3Department of Energy Technology, Aalborg University, Denmark inam0003 @e.ntu.edu.sg

Abstract - In an autonomous microgrid where centralized

management and communication links are not viable, droop

control has been the preferred scheme for power sharing among

distributed generators (DGs). At present, although many droop

variations have been proposed to achieve proportional power

sharing based on the DG kV A ratings. Other operating

characteristics like generation costs, efficiencies and emission

penalties at different loadings have not been considered. This

makes existing droop schemes not too well-suited for standalone

microgrids without central management system, where different

types of DGs usually exist. As an alternative, this paper proposes

a cost-based droop scheme, whose objective is to reduce a

generation cost realized with various DG operating

characteristics taken into consideration. The proposed droop

scheme therefore retains all advantages of the traditional droop

schemes, while at the same time keep its generation cost low.

These findings have been validated through simulation and

scaled down lab experiment.

Index Terms- Microgrids, distributed generation, droop

control, autonomous control, power converters.

I. I NTRODUCTION

Distributed generators (DGs), when clustered to form small microgrids, offer many advantages like resource optimization, improved power quality, stability and reliability [1]-[3]. The formed microgrids can certainly be controlled by centralized management systems [3]-[5], but for widely dispersed DGs where communication links are not viable, autonomous droop schemes might be more appropriate. So far, the common objective focused by the droop schemes has been proportional power sharing among the DGs based on their respective kV A ratings [5]-[6]. This objective is no doubt fme if the DGs are of the same type just like in the earlier control of parallel synchronous generators [7], uninterruptible power supplies [8] and interlinked ac microgrids [9]-[10]. It is however usually not the case for standalone microgrids, where different types of DGs havmg different cost functions and emission characteristics usually exist, like for an example microgrid shown in Fig I. Proportional power sharing based on ratings alone might therefore not be sufficient or appropriate for microgrids. Other factors like costs, efficiencies, pricing schedules and emission penalties should rightfully be considered just like in

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most centralized cases, where power dispatch commands are usually decided from a combination of factors rather than ratings alone [3]-[5]. The same thought has however never been tried with droop control for an autonomous islanded microgrid.

To address the concern raised above, a cost-based droop scheme has been proposed, whose power sharing in the steady state will result in a lower total generation cost (TGCi for the microgrid, as compared to the traditional droop schemes. The proposed scheme methodology, simulation and experimental findings are given in subsequent sections followed by review of traditional droop scheme.

II. TRADITIONAL DROOP SCHEME

The basic droop scheme explained in the literature is based on the two linear expressions written in (1) and (2), where x, I, V, {P, Q and S}, and {max and min} are the DG unit number, frequency, terminal voltage, active, reactive and apparent power generations, and their corresponding maximum and minimum values, respectively. Also included in the two expressions are the active wand reactive u droop coefficients, which no doubt are just the gradients of the two droop lines. Implementation of the two droop lines would generally mvolve measuring the DG terminal voltages and currents for computmg its active and reactive power generations [11]-[12]. The obtamed powers Px and Qx can then be substituted into (1) and (2) to obtain the frequency Ix and voltage Vx references for forming a set of three-phase sinusoidal commands. The sinusoidal voltages can finally be tracked by a standard multi- or single-loop controller, whose design can be found in [5],[13].

Ix = Imax- wxPx; w - fmax-f min (1) x- Sx,max

Vx = Vmax - uxQx Vmax-Vmin (2) , Ux = SX,max Many variations have since been extended from the two

basic droop lines, whose common objective is still to mamtain proportional power sharmg based on the DG ratmgs

i TGC is used here to refer to a weighted combination of factors like fuel, emission, maintenance and operational costs, which rightfully can be freely tuned by the users and/or operators

[5]-[12],[14]-[15]. For (1) and (2), it would mean setting the droop coefficients according to (3) and (4).

WISI,max = W2S2,max = . . . = WxSx,max = . . . = [max - [min (3)

To demonstrate the effectiveness of (3) and (4), a simple microgrid with three DGs is considered, which in the steady state, will share a single common network frequency [ (= [1 = [2 = [3)' Substituting [ into (1) leads to (5), which would force the higher rated DG to produce more active power in order to satisfy the equality. The same principle can be applied to reactive power sharing, whose resulting expression is shown in (6). In (6), the equality shown is only approximate due to the practical fact that terminal voltages of DGs will never be exactly equal in the steady state. This imperfection has led to many variations, whose sole objective is to improve on reactive power sharing based again on ratings.

PI P2 P3 51,max 52. max 53•max

����� 51,max 52,max 53,max

III. PROPOSED COST-BASED DROOP SCHEME

(5)

(6)

Although tried by many researchers and proven effective, the traditional droop scheme based only on ratings might not be suitable for microgrids with different types of DGs. In addition, it should be mentioned that most droop schemes proposed so far have always been based on those linear expressions shown in (1) and (2). It is certainly not a strict requirement, meaning that nonlinear droop curves can also be used for the intended autonomous control. This is in fact the case for the proposed droop scheme based on reducing the TGC of the overall microgrid. Details of the scheme are discussed as follows.

A. Generation Cost Curves Generation costs of a DG can include many factors, which

in general, can be grouped under two categories named as operating cost Cx,o(Px) and emission penalty-incentive cost Cx,((Px)' When added together like in (7), the TGC of each DG represented by Cx (Px) can rightfully be drawn as a quadratic function.

(7)

Referring back to the operating cost, fuel costs of a diesel generator driven by an internal combustion engine or a DG driven by a micro-turbine can usually be represented by a second-order quadratic function [16]-[18]. Adding to these is a second set of quadratic functions, whose purposes are to account for emission penalties faced by the engine or turbine driven generator or incentives rewarded to the renewable DG [17]-[18].

Fig. 1. Three DGs example microgrid

The similar function can also be derived to represent total generation costs of a dispatch-able renewable DG such as fuel cell, wind or photovoltaic with storage even though it is derived differently, by adding the direct or fix operating cost and emission penalty/incentive cost and then dividing it by inverter loss-efficiency function [19]-[21].

To illustrate, TGC curves of two engine driven DGs (CI and C2) and one renewable DG ( C3 ) for the example microgrid shown in Fig 1 are plotted in Fig. 2(a), where the cost function (y-axis) of the DGs has been normalized and plotted against the P� (x-axis). The definition of the normalized cost and power is given by (8) and (9), respectively.

C' (P ) - Cx(Px) _ Cx(Px) x x - Px,max - Px,rated

p'=�=� X PX,max px.rated

(8)

(9)

The cost nonnalization in (8) based on individual DG maximum/rated power (Px,max)helps to place the cost ofDGs within a common range for comparison on equal scale regardless ofDGs different kVA rating.

Further it shall be noted that at zero P�, the costs are noted to be non-zero. These no-load costs are always there so long as their associated droop controlled DGs are operating. Being independent of P� , they should be removed from consideration when deciding on the amount of active power generation. The modified cost curves shown in Fig. 2(b) can hence be represented by (10).

C;(Px) = C�(Px) - C�(Px = 0) (10)

B. Cost Based Droop Methodology Using the generation cost function given in (10), the

proposed droop scheme is expressed as: k = imax-i min x

max(C�max) (11)

340

0.3 -., � 0.2

-\,.)� '" a 0.1 0.0602

10����======:

C=�::===========

0.=0=5 1J 0 �·03476

0.2 0.4 0.6 0.8

0.3,--�--�--�--�--,

), 0.2 � � � 0.1

0.2

0.199

0.4 0.6 0.8 Active Power p' Active Power p'

x x

w � Fig. 2. Generation cost curves of DGs (a) C�(Px)and (b) C�(Px)

51

r-=�;;;;:-----.!.�_J � � 50.5

50 49.7511z

49L---�------�----�----�L-L-� 0.2 0.4 0.6

Active Power p' x

0.8

51.5 r---�----�------�----�-------'

� 51 r=::�:::::::� __ � -: 50.5 c-� 50 � tt 49.5

49 L---�----�------�L---LL----� 0.2 0.4 0.6

A ctive Power p' x

0.8

w � Fig. 3. Frequency versus power curves for the cost-based droop scheme with (a) max (C�.max) and (b) C�

.max in the denominator of kx

In (11), the max( ) function is used to extract the highest maximwn generation cost among the DGs when they are at the 100% generation limit (P; = 1). Applying it to the example microgrid with three DGs of cost curves shown in Fig 2(b), results in:

lower cost objective and other parameter limits to be discussed next.

(14)

k - k - k - imax-imin - imax-imin (12) C. Parameter Limits

1 - 2 - 3 - maxCC�max) c�:max C�'CPl) = C�'CP2 ) = C�'CP3 ) (13)

To satisfy the equality in (13), it simply means that the DG with the lowest TGC would produce more and vice versa. Pictorially, it can also be seen by either drawing a horizontal constant cost line in Fig. 2(b) or a horizontal constant frequency line in Fig. 3(a). The overall TGC of the microgrid can hence be an addition of three DGs TGC, which will surely be lower than that produced by the traditional droop scheme. From the understanding gained from (13), it should rightfully be mentioned too that the denominator of kx in (11) should not be mistaken as G.max. Else, the resulting equality will become (14), which will also depend on the individual maximum TGCs of the DGs when at full-loadCP; = 1). This dependence is not encouraged since it causes the DG with the lowest TGC to produce less active power in order to give a smaller C;CPx) to counter the smaller Gmax . This shortcoming can also be seen by drawing a horizontal line across Fig. 3(b), which shows the cost curves plotted with (9), but with the denominator of kx replaced by C�.max' It is hence important to set kx appropriately in order to meet the

341

Substituting (12) to (11) for the example microgrid with three DGs leads to the following expression.

F F C;CPx) C F F ) lmin = lmax - � lmax - lmin ; X = 1,2 or 3 (15) 1,max

The maximum frequency [max is obviously arrived at when P; = 0 and hence C;CPx) = 0 according to the cost curves drawn in Fig. 2(b). On the other hand, the minimum frequency [min is arrived at when the most costly DG is operating at its full-loadCP� = 1). For the example microgrid, it happens when C;CPx) = C�',max' which confIrms that the proposed droop scheme can operate within the defined frequency range from [min to [max' It should however be noted that the minimum frequency [min is somehow not reached by the other two less costly DGs since their maximum costs at the full-load is lesser than C�,max' Their respective frequencies at full-load are hence higher than [min but smaller than [max according to those cost curves drawn in Fig. 3(a). Because of that, for a common steady state frequency close to [min, active power outputs of the two lower cost DGs must be limited to P;,max (or lower), which in practice can be done by adding a simple proportional-integral controller (16) to (11).

Simulation Results o.8,------,------,---,---,------,,-----

°0�-�---4L- -�6- --L--�10- -�12 Time(vec)

Experiment Results

°O�--5�O�-�1�OO�-1�5�O��2�O�O-�2�50�-�300 Tillie (sec)

00 00 Fig. 4. Variation of micro grid TGC(PJ as load changes with traditional and cost-based droop scheme (a) simulation and (b) experiment results

. " 1 '" � 0.8 � 0.6 .�

0.4· �9������:t=====j t -.: 0.2·

°OL--�--L--�---L--�10---12 Time(sec) Thne (sec) 00 00

Fig. S. Variations of DG active powers as load changes in the cost-based droop scheme (a) simulation and (b) experiment results. 51.5 ,-------r---,----,----...,---�-__, 51 >l' 51 : 50.87

� 50.5 � 505 -..," �" . c- 50 "' 50 � � S. 49.5 � 49.5 � <t 49 48.5 48.5 0 12 0 300

nme (,w�c) 00 00

Fig. 6. Variations of micro grid frequency as load changes in the cost-based droop scheme (a) simulation and (b) experiment results.

Ix = (p�.max - px') X (Kp + Ki/S); Px' � P�,max (16)

where Kp and Ki are the proportional and integral gains, respectively.

IV. SIMULATION RESULTS

To illustrate the effectiveness of the proposed cost-based droop scheme, the example microgrid shown in Fig. 1 was simulated in Matlab/Simulink software. The DGs rating and other system parameters are given in TABLE I. Their respective cost and droop curves are similar to those shown in Fig. 2(a) and Fig. 3(a), which when applied to (11), lead to kl = k 2 = k3 = _

2_ = 8.16. With these defined parameters, 0.245

the proposed droop scheme is verified with three different loading conditions 30%(Iow), 6O%(moderate) and 90%(heavy) of the total microgrid generation capacity. Figure 4(a) shows the corresponding microgrid total generation cost obtained with the cost-based and traditional droop schemes, where the fonner clearly shows a reduction in TGC for the studied microgrid. The saving is, as anticipated, achieved by forcing the low-cost DG to produce more and the high-cost DG to produce less. According to Fig. 2(b), the low-cost DG will always be unit 3, while the high-cost DG will be unit 2 from 0 to 60% loading (P� = 0.6), and then unit 3 from 60% loading ( P� = 0.6) onwards. This is

342

certainly in agreement with Fig. 5(a), which shows the individual DG active outputs for the three loading conditions. Their corresponding common frequency variation is also shown in Fig. 6(a) for easier correlation of events happened during the three load intervals.

TABLE I MJCROGRlD SYSTEM PARAMETERS Parameters

{min H {max Vmin H Vmax

Phases Max. Pl, = P2 = P3 Max. Ql = Q2 = Q3

Max. P; and Q� Base Power 5 Base Voltage

kl = k2 = k3 (�,max

Values

49 H SlHz

0.9SpUH 1.0Spu 3

IkW 0.7SkVAr 1.0 each 1 kVA 190.S 8.16

shown in Fig 2(b)

From the presented figures, it should also be mentioned that the 14% saving in TGC for the second loading condition in Fig. 3 is greater than the 2% saving experienced in the first interval. This is undeniably the case as differences in the cost curves become more prominent at higher loading condition. An increase in saving is however not observed in the third interval during which the load has further increased. The reason for that is due to the saturation of DG unit 3 at its rated value (full-load), which to a sizable extent, has hindered its

contribution to saving even though it has the lowest cost. The saving in the third interval has hence dropped from 14% to 6.8% in Fig. 3, which after all is still a saving as compared to the traditional scheme.

V. EXPERIMENTAL RESULTS

The microgrid DGs and loads shown in Fig 1 were emulated using digitally controlled three phase inverters and variable active and reactive load banks. The DGs rating, frequency, cost curves and other parameters were set same as described in section IV, also given in TABLE I. The experiment was carried with three different loading conditions. However, the total % load in all three intervals was not exactly same as simulation cases, this relatively higher loading during experiment can be observed from the cost and power values shown in Fig. 4 and Fig. 5. The experiment results for TGC saving, power sharing among

DGs agrees with the proposed scheme theoretical findings and simulation results, as shown in Fig. 4(b) to Fig 5(b). The experimental results for microgrid frequency variation are also shown Fig. 6(b).

VI. CONCLUSION

A cost-based droop scheme has been proposed for autonomous microgrid applications with different types of DGs considered. Instead of relying only on the DG power ratings, the proposed scheme arrives at a steady-state power sharing based on various cost factors grouped under the general term of TGC. The goal is to reduce the overall microgrid TGC without affecting the simplicity of the droop scheme. Effectiveness of the proposed scheme has been dually verified through simulation and scaled-down lab experiment.

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